2021 Fall AMC 12A Problems/Problem 19
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Problem 19
Let be the least real number greater than
such that sin
= sin
, where the arguments are in degrees. What is
rounded up to the closest integer?
Solution 1
The smallest to make
would require
, but since
needs to be greater than
, these solutions are not valid.
The next smallest would require
, or
.
After a bit of guessing and checking, we find that , and
, so the solution lies between
and
, making our answer
Note: One can also solve the quadratic and estimate the radical.
~kingofpineapplz